Variance

What is Variance in Statistics?

Variance meaning – It is a measure of how data points differ from the mean. According to layman’s terms, it is a measure of how far a set of data( numbers) are spread out from their mean (average) value.

For the purpose of solving questions, it is,

Var (X) = E[ ( X – \(\mu\)))2]

Put into words; this means that variance is the expectation of the deviation of a random set of data from its mean value, squared. Here,

“µ” is equal to E(X) so the above equation may also be expressed as,

Var(X) = E[(X – E(X)2)]

Var(X) = E[ X2 -2X E(X) +(E(X))2]

Var(X) = E(X2) -2 E(X) E(X) + (E(X))2

Var(X) = E(X2) – (E(X))2

Now let’s have a look at the relationship between Variance and Standard Deviation.

Standard Deviation is a measure of how spread out the data is. Its formula is simple; it is the square root of the variance for that data set. It’s represented by the Greek symbol sigma( ).

Learning with Example:

The concepts mentioned above sound a little boring don’t they? The concept of statistics often appears this way since it means dealing with large volumes of data; It is essential that you, as a student, understand that these are not just numbers; If read properly, it tells you a story. So let’s take a fun example of how to calculate variance in everyday life situation: